Abstract

The intrinsic weak birefringence in all-normal dispersion highly nonlinear fiber, particularly ultra-high-numerical-aperture fiber, generates supercontinuum with long term polarization instabilities, even for seed pulses launched along the perceived slow axis of the fiber. Highly co/anti-correlated fluctuations in energy between regions of power spectral density mask the extent of the spectral noise in total integrated power measurements. The instability exhibits a seed pulse power threshold above which the output polarization state of the supercontinuum seeds from noise. Eliminating this instability through the utilization of nonlinear fiber with a large designed birefringence, encourages the exploration of compression schemes and seed sources. Here, we include an analysis of the difficulties for seeding supercontinuum with the highly attractive ANDi-type lasers. Lastly, we introduce an intuitive approach for understanding supercontinuum development and evolution. By modifying the traditional characteristic dispersion and nonlinear lengths to track pulse properties within the nonlinear fiber, we find simple, descriptive handles for supercontinuum evolution.

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References

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    [CrossRef] [PubMed]
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2012

2011

2008

2007

2006

2004

1995

1988

S. Wabnitz, “Modulation polarization instability of light in a nonlinear birefringent dispersive medium,” Phys. Rev. A38, 2018–2021 (1988).
[CrossRef] [PubMed]

1986

H. G. Winful, “Self-induced polarization changes in birefringent optical fiber,” Appl. Phys. Lett.47, 213–215 (1986).
[CrossRef]

Aus-der-Au, J.

Bartels, R.

Bartelt, H.

Boppart, S.

Boppart, S. A.

Bosman, G.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, NY, 2003).

Brown, T.

Buckley, J.

Champert, P.

Chong, A.

Clay, G.

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys.78, 1135–1184 (2006).
[CrossRef]

Couderc, V.

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys.78, 1135–1184 (2006).
[CrossRef]

Finot, C.

Froehly, C.

Fvrier, S.

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys.78, 1135–1184 (2006).
[CrossRef]

Hartung, A.

Harvey, J.

Heidt, A.

Hooper, L.

Kane, D. J.

Kibler, B.

Kleinfeld, D.

Knight, J.

Koh, Y.

Krok, P.

Labont, L.

Leonhardt, R.

Leproux, P.

Lgsgaard, J.

Limpert, J.

Liu, X.

Liu, Y.

Marks, D.

Marks, D. L.

Millard, A.

Mosley, P.

Muir, A.

Murdoch, S.

Nrin, P.

Oldenburg, A. L.

Provost, L.

Renninger, W.

Reynolds, J. J.

Rohwer, E.

Rothhardt, J.

Roy, P.

Schaffer, C.

Schlup, P.

Schwoerer, H.

Squier, J.

Tnnermann, A.

Tombelaine, V.

Tsai, P.

Tu, H.

Turchinovich, D.

Wabnitz, S.

Wadsworth, W.

Wilson, J.

Winful, H. G.

H. G. Winful, “Self-induced polarization changes in birefringent optical fiber,” Appl. Phys. Lett.47, 213–215 (1986).
[CrossRef]

Wise, F.

Zhu, Z.

Appl. Phys. Lett.

H. G. Winful, “Self-induced polarization changes in birefringent optical fiber,” Appl. Phys. Lett.47, 213–215 (1986).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

J. Wilson, P. Schlup, and R. Bartels, “Ultrafast phase and amplitude pulse shaping with a single, one-dimensional, high-resolution phase mask,” Opt. Express15, 8979–8987 (2007).
[CrossRef] [PubMed]

A. Chong, J. Buckley, W. Renninger, and F. Wise, “All-normal-dispersion femtosecond fiber laser,” Opt. Express14, 10095–10100 (2006).
[CrossRef] [PubMed]

A. Heidt, J. Rothhardt, A. Hartung, H. Bartelt, E. Rohwer, J. Limpert, and A. Tnnermann, “High quality sub-two cycle pulses from compression of supercontinuum generated in all-normal dispersion photonic crystal fiber,” Opt. Express19, 13873–13879 (2011).
[CrossRef] [PubMed]

A. Heidt, A. Hartung, G. Bosman, P. Krok, E. Rohwer, H. Schwoerer, and H. Bartelt, “Coherent octave spanning near-infrared and visible supercontinuum generation in all-normal dispersion photonic crystal fibers,” Opt. Express19, 3775–3787 (2011).
[CrossRef] [PubMed]

P. Champert, V. Couderc, P. Leproux, S. Fvrier, V. Tombelaine, L. Labont, P. Roy, C. Froehly, and P. Nrin, “White-light supercontinuum generation in normally dispersive optical fiber using original multi-wavelength pumping system,” Opt. Express12, 4366–4371 (2004).
[CrossRef] [PubMed]

L. Hooper, P. Mosley, A. Muir, W. Wadsworth, and J. Knight, “Coherent supercontinuum generation in photonic crystal fiber with all-normal group velocity dispersion,” Opt. Express19, 4902–4907 (2011).
[CrossRef] [PubMed]

H. Tu, Y. Liu, X. Liu, D. Turchinovich, J. Lgsgaard, and S. Boppart, “Nonlinear polarization dynamics in a weakly birefringent all-normal dispersion photonic crystal fiber: toward a practical coherent fiber supercontinuum laser,” Opt. Express20, 1113–1128 (2012).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

S. Wabnitz, “Modulation polarization instability of light in a nonlinear birefringent dispersive medium,” Phys. Rev. A38, 2018–2021 (1988).
[CrossRef] [PubMed]

Rev. Mod. Phys.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys.78, 1135–1184 (2006).
[CrossRef]

Other

R. W. Boyd, Nonlinear Optics (Academic, NY, 2003).

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Figures (8)

Fig. 1
Fig. 1

(a) SC spectral phase from 4 nJ 350 fs seed pulses for different fiber lengths with the transform limit and power spectrum inset. Evolution of the (b) power spectrum (c) residual spectral phase after GDD compensation (residual phase set to −5 outside of the −20 dB power spectral envelope) and (d) local and accumulated characteristic lengths all as a function of fiber length. The local dispersion length and accumulated dispersion lengths, χD, are in blue and the local nonlinear length and accumulated nonlinear length, χNL, are in black. The calculated length for the onset of WB, 62 mm, is included as the vertical dashed white line in (b) and (c) and dashed black line in (d)

Fig. 2
Fig. 2

The peak power evolution with χD for 4 nJ 100 fs (a), 200 fs (b), and 300 fs (c) seed pulses and GDD compensation in black and complete compensation to the transform limit in red. The onset of WB is plotted in (a)–(c) as a dashed vertical line. (d) The transform limited pulse duration in red and the pulse duration with only GDD compensation in black markers as functions of χD for 4 nJ pulses and a suite of seed pulse durations: 100 – 350 fs. The solid black markers indicate the evolution up to the maximum peak power enhancement with GDD compensation, followed by hollow markers for additional propagation. The fiber length corresponding to the maximum peak power enhancement with GDD compensation as a function of χD (e) for a suite of seed pulses: 2, 4, and 6 nJ shown in blue, black, and green respectively, and pulse durations from 100–350 fs. The maximum peak power enhancement factor with GDD compensation, relative to the incident seed pulses (composed of twice the energy), and the accumulated nonlinear length at peak enhancement(f).

Fig. 3
Fig. 3

(a) The peak power evolution as a function of fiber length for 6 nJ 100 fs seed pulses with GDD compensation in black and GDD and TOD compensation in green. The compressed SC intensity is shown at several fiber lengths and compensation orders in inset Figs. (a1)–(a4). The SHG and THG signal enhancement relative to the incident 12 nJ 100 fs pulse, as a function of fiber length and order of compensation: transform limited in blue, GDD and TOD in green, and GDD in black.

Fig. 4
Fig. 4

(a) Phantom SHG-FROG and (b) reconstructed spectrogram

Fig. 5
Fig. 5

SC time series for (a) 200 mW, (b) 300 mW, (c) 375 mW, and (d) 300 mW (after 4.5 hours of fiber warm-up) coupled power in UHNA-3 fiber. The mean power spectrum (shaded blue), RSN (solid black), ΦRSN (dashed black), and RMS-N (dashed-green) in (e) and (f) from the time series (d) and (c), respectively.

Fig. 6
Fig. 6

SC time series (a) and (b) power spectrum (blue), RSN (solid black), ΦRSN (dashed black), and RMS-N (dashed-green) for the 45 minute time interval in (a) from 375 mW average coupled power into CorActive PM UHNA fiber. The Phantom SHG-FROG (c), the SC reconstructed power spectrum (black) and spectral phase (dashed-black), and seed power spectrum (blue) in (d). The normalized seed intensity (blue) and the reconstructed SC intensity after a two stage compression system (e).

Fig. 7
Fig. 7

The power spectrum (a) and intensity, labeled GDD, (b) of the ANDi seed pulse reconstructed with SHG-FROG. Also in (b) are ANDi pulse intensities with up to TOD and FOD spectral phase compensation along with the transform limit. The peak power evolution with χD of SC with GDD compensation (black) and the transform limited SC (red) for some of the ANDi seed pulses in (b): FOD (c), TOD (d), and GDD (e). The onset of WB is plotted in (c) as a dashed vertical line.

Fig. 8
Fig. 8

SC time series (a) and mean power spectrum (shaded blue), RSN (solid-black), ΦRSN (dashed-black), and RMS-N (dashed-green) (b) from 45 minute time intervals from ANDi seeds and 190 mW couple power. (c) The ANDi oscillator mean power spectrum (shaded blue), RSN (solid-black), ΦRSN (dashed-black), and RMS-N (dashed-green)

Equations (3)

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z WB = L D ( z = 0 ) 4 exp ( 3 / 2 ) N 2 1
L D ( z ) = τ ( z ) 2 | β 2 | , L NL ( z ) = 1 γ 0 P ( z )
Φ RSN = σ ( λ ) μ ( λ ) d λ μ 2 ( λ ) d λ

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